Searching further, I found the delegate BindLambda. This allows me to create a callback and have my different outputs. What do you think?
Request->OnProcessRequestComplete().BindLambda([Callback](FHttpRequestPtr Request, FHttpResponsePtr Response, bool bWasSuccessful)
{
Callback.ExecuteIfBound(Response->GetContentAsString(), Response->GetResponseCode(), bWasSuccessful);
});
